a-k.com/glossary

Dreamghast (_youmu_)
Dreamghasts are bizarre creatures that wander the earth. Their forms are multifarious, and nobody knows where they come from.
Some of them eat humans. Ordinary people can't see them.

Xenor (_ikaishi_)
Xenors are people whose job it is to slay dreamghasts. Their powers are passed on by blood.

the Xenor Conclave (_ikaishi kyoukai_)
The Xenor Conclave is an association to which all xenors belong.
One is recognized as a xenor only after registering with the Conclave. Nobody knows who founded it, or why.

Ghastrock (_youmu-seki_)
When a dreamghast is eliminated, it leaves behind a ghastrock. They come in many shapes and sizes, and nobody knows much about them.
According to one theory, a ghastrock might be a dreamghast's nucleus.
Once appraised, xenors can cash them for a reward.

Half-ghast (_han-you_)
Half-ghasts are said to be an exotic sort of being, born to a human and a dreamghast. However, since they are so rare, little is known about them.

the Nase family
The Nase family is a lineage of cage-controllers. Since long ago, they have administered Nagatsuki and its vicinity.

Nodera Town, Nagatsuki City
Where Akihito and the rest live.